Polar and quadrupolar order in smectic liquid crystals

In several smectic phases the long molecules are tilted towards the layer planes. The molecules in the layers of smectic C phases have a preferred tilt direction with a C2 rotation axis perpendicular to the tilt plane. If the molecules have a brick-like shape, a configuration possessing the D2h symmetry is also possible. For molecules shaped like chevrons or bananas, the existence of a smectic phase with the symmetry Cv was recently reported. We consider different in-plane configurations of smectics using a geometrical approach based on the 'scaled particle theory'. Varying the geometrical parameters of hard rod particles, a phase diagram for several smectic configurations is predicted. Depending on the particle shape, phases with dipolar order (C2,Cv) and quadrupolar order (D2h) can be stable.